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1.

図書

図書
George Boros, Victor Moll
出版情報: Cambridge, UK : Cambridge University Press, 2004  xiv, 306 p. ; 24 cm
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2.

図書

図書
I.S. Gradshteyn and I.M. Ryzhik
出版情報: San Diego ; Tokyo : Academic Press, c2015  xlv, 1133 p. ; 25 cm
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3.

図書

図書
Henry McKean, Victor Moll
出版情報: New York : Cambridge University Press, 1997  xiii, 280 p. ; 24 cm
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目次情報: 続きを見る
Preface
First Ideas: Complex Manifolds, Riemann Surfaces, and Projective Curves / 1.:
The Riemann Sphere / 1.1:
Complex Manifolds / 1.2:
Rational Functions / 1.3:
Luroth's Theorem / 1.4:
Automorphisms of P[superscript 1] / 1.5:
Spherical Geometry / 1.6:
Finite Subgroups and the Platonic Solids / 1.7:
Automorphisms of the Half-Plane / 1.8:
Hyperbolic Geometry / 1.9:
Projective Curves / 1.10:
Covering Surfaces / 1.11:
Scissors and Paste / 1.12:
Algebraic Functions / 1.13:
Examples / 1.14:
More on Uniformization / 1.15:
Compact Manifolds as Curves: Finale / 1.16:
Elliptic Integrals and Functions / 2.:
Elliptic Integrals: Where They Come From / 2.1:
The Incomplete Integrals Reduced to Normal Form / 2.2:
The Complete Integrals: Landen, Gauss, and the Arithmetic-Geometric Mean / 2.3:
The Complete Elliptic Integrals: Legendre's Relation / 2.4:
The Discovery of Gauss and Abel / 2.5:
Periods in General / 2.6:
Elliptic Functions in General / 2.7:
The and-Function / 2.8:
Elliptic Integrals, Complete and Incomplete / 2.9:
Two Mechanical Applications / 2.10:
The Projective Cubic / 2.11:
The Problem of Inversion / 2.12:
The Function Field / 2.13:
Addition on the Cubic / 2.14:
Abel's Theorem / 2.15:
Jacobian Functions: Reprise / 2.16:
Covering Tori / 2.17:
Finale: Higher Genus / 2.18:
Theta Functions / 3.:
Jacobi's Theta Functions / 3.1:
Some Identities / 3.2:
The Jacobi and Weierstrass Connections / 3.3:
Projective Embedding of Tori / 3.4:
Products / 3.5:
Sums of Two Squares / 3.6:
Sums of Four Squares / 3.7:
Euler's Identities: Partitio Numerorum / 3.8:
Jacobi's and Higher Substitutions / 3.9:
Quadratic Reciprocity / 3.10:
Ramanujan's Continued Fractions / 3.11:
Modular Groups and Modular Functions / 4.:
The Modular Group of First Level / 4.1:
The Modular Group of Second Level / 4.2:
Fundamental Cells / 4.3:
Generating the Groups / 4.4:
Gauss on Quadratic Forms / 4.5:
The Group of Anharmonic Ratios / 4.6:
Modular Forms / 4.7:
Eisenstein Sums / 4.8:
Absolute Invariants / 4.9:
Triangle Functions / 4.10:
The Modular Equation of Level 2 / 4.11:
Landen's Transformation / 4.12:
Modular Equations of Higher Level / 4.13:
Jacobi's Modular Equation / 4.14:
Jacobi and Legendre's Derivation: Level 5 / 4.15:
Arithmetic Subgroups: Overview / 4.16:
Ikosaeder and the Quintic / 5.:
Solvability of Equations of Degree [less than] 4 / 5.1:
Galois Groups Revisited / 5.2:
The Galois Group of Level 5 / 5.3:
An Element of Degree 5 / 5.4:
Hermite on the Depressed Equation / 5.5:
Hermite on the Quintic / 5.6:
A Geometric View / 5.7:
Imaginary Quadratic Number Fields / 6.:
Algebraic Numbers / 6.1:
Primes and Ideal Numbers / 6.2:
Class Invariants and Kronecker's Jugendtraum / 6.3:
Application of the Modular Equation / 6.4:
The Class Polynomial / 6.5:
Class Invariants at a Prime Level / 6.6:
Irreducibility of the Class Polynomial / 6.7:
Class Field and Galois Group / 6.8:
Computation of the Class Invariants / 6.9:
Arithmetic of Elliptic Curves / 7:
Arithmetic of the Projective Line / 7.1:
Cubics: The Mordell--Weil Theorem / 7.2:
Proof of the Mordell--Weil Theorem / 7.3:
References
Index
Preface
First Ideas: Complex Manifolds, Riemann Surfaces, and Projective Curves / 1.:
The Riemann Sphere / 1.1:
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